Theoretical description of the polymerase chain reaction

Taking into account expressions for the efficiency of the polymerase chain reaction (PCR) recently deduced from enzymological considerations, and making use of a continuous model based on the law of mass action, closed form solutions are derived that enable a complete description of the standard and quantitative competitive PCR methods. The resulting behaviour is in reasonable agreement with that from a previous, empirical, discrete approach; but the latter is nonetheless shown to overestimate the amplification yield by as much as 30% due to the weak assumption of a constant efficiency during the cycle duration. The present formalism will facilitate the implementation of accurate fitting procedures of experimental data to manage quantification.